
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]


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A flock of 155 birds sit down on a circle \( C \). Two birds \( P_{i}, P_{j} \) are mutually visible if \( m(P_{i} P_{j}) \leq 10^\circ \). Find the smallest number of mutually visible pairs of birds. (One assumes that a position (point) on \( C \) can be occupied simultaneously by several birds.)

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