
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
155 birds  $ P_1, \ldots, P_{155}$  are sitting down on the boundary of a circle  $ C.$  Two birds  $ P_i, P_j$  are mutually visible if the angle at centre  $ m(\cdot)$  of their positions  $ m(P_iP_j) \leq 10^{\circ}.$   Find the smallest number of mutually visible pairs of birds, i.e. minimal set of pairs  $ \{x,y\}$  of mutually visible pairs of birds with  $ x,y \in \{P_1, \ldots, P_{155}\}.$  One assumes that a position (point) on  $ C$  can be occupied simultaneously by several birds, e.g. all possible birds.

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