
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  $A_1A_2A_3 \ldots A_{21}$  be a 21-sided regular polygon inscribed in a circle with centre  $O$ . How many triangles  $A_iA_jA_k$ ,  $1 \leq i < j < k \leq 21$ , contain the centre point  $O$  in their interior?

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