
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
A circle of radius  $R$  is divided into  $8$  equal parts. The points of division are denoted successively by  $A, B, C, D, E, F , G$  and  $H$ . Find the area of the square formed by drawing the chords  $AF$  ,  $BE$ ,  $CH$  and  $DG$ .

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