
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
 $AB$  is a chord of length  $6$  in a circle of radius  $5$  and centre  $O$ . A square is inscribed in the sector  $OAB$  with two vertices on the circumference and two sides parallel to  $ AB$ . Find the area of the square.

Present the answer in LaTex format: \boxed{Your answer}
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