
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
In a convex pentagon, all the diagonals are drawn. For each pair of diagonals that intersect inside the pentagon, the smaller of the angles between them is found. What values can the sum of these five angles take?

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