Raid on Reach

The Second Battle of Reach was a small operation conducted by the UNSC survivors of the Battle of Installation 04, trying to find a viable way to return to UNSC controlled space. It turned into a rescue operation when they determined that Spartans were still alive and on Reach.

That Battle was a testing ground for multiple improvements Cortana had made to Covenant technology

The Installation 04 Survivors
Having captured the Covenant Flagship Ascendant Justice, they were in a position where they could not return to Human controlled space due to Article 7 of the Cole Protocol. The Article required that a captured Covenant vessel be thoroughly searched for any tracking devices that would alert the Covenant to a new Human controlled system before that vessel could enter a System that the Covenant weren't aware of.

The decision was made to set course for Reach for several reasons:
 * 1) Reach was a known system to the Covenant, so it would not be in violation of the Cole Protocol
 * 2) There may be a functional warship after the Battle of Reach that they might be able to use to get to UNSC controlled space
 * 3) There was a chance of survivors being found

Covenant
Unlike most of their operations, Covenant forces had chosen to only selectively bomb Reach rather than glass the planet. The reason for this was that they were particularly interested in Forerunner artifacts, particularly a Forerunner crystal that they called the "Holy Light". As a result, at least two (if not more) groups of survivors remained on the planet.

Admiral Whitcomb
During the Battle of Reach, 3 Spartans (names) joined up with Vice Admiral Whitcomb. After planting a NOVA bomb inside the Covenant ranks, they spent the next several weeks performing Guerrilla Attacks upon occupational Covenant forces on Reach. However, they were stranded on the planet.

Dr Halsey
Underneath the ruins of CASTLE base, Dr. Halsey and 5 Spartans (Fred, Kelly, Will, Vinh, Issac) had spent 5 days combing the remains of a Forerunner base and an additional 5 days trapped in a hallway inside the ruins by Covenant forces. Vinh and Issac had both fallen by the time the Second Battle of Reach had begun.

Arrival at Reach
The Ascendant Justice arrived seven hundred thousand kilometers from Reach where her crew assessed the situation. They noticed several of ships in orbit along with an orbital docking station and that the planet had mostly been glassed. However, a small spot that had not been destroyed perked the interest of both the John-117 and Lieutenant Haverson, the former because it meant that there might be survivors from the Spartan team, the latter because of the Covenant's obvious interest in that spot.

When they arrived at Reach, they sent all the standard responses to indicate that they were still Covenant controlled. The Ascendant Justice was supposed to have a high ranking person on board so the Covenant did not question their authority to be there and thus, the charade proceeded. From here, they were able to determine that the enemy fleet consisted of a dozen Cruisers and a pair of Carriers. They also spotted a pile of debris where all the leftover Covenant and UNSC ships that had fallen in the Battle of Reach were being kept. They also picked up a weak transmission which the Master Chief, alone, recognized it: it was the Spartan Oly Oly Oxen Free signal. From this, he knew that there were Spartans alive on the planet.

Aftermath
The survivors of the Second Battle of Reach would eventually fight in Operation: FIRST STRIKE.