
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
Let  $P$  be a point outside a circle  $\Gamma$  centered at point  $O$ , and let  $PA$  and  $PB$  be tangent lines to circle  $\Gamma$ . Let segment  $PO$  intersect circle  $\Gamma$  at  $C$ . A tangent to circle  $\Gamma$  through  $C$  intersects  $PA$  and  $PB$  at points  $E$  and  $F$ , respectively. Given that  $EF=8$  and  $\angle{APB}=60^\circ$ , compute the area of  $\triangle{AOC}$ .

*2020 CCA Math Bonanza Individual Round #6*

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