
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
The plate has the shape of a regular hexagon \(ABCDEF\) with side \(a\). \(O\) is the center of the hexagon. A square \(OMAN\) is cut out from the plate, with \(OA\) as one of its diagonals. Determine the distance from \(O\) to the center of gravity of the remaining plate.

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