
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
An angle ∠BAC is said to be "laceable" if distinct points X1, X2, ..., X2n can be found such that X2k-1 is on AC for each value of k, X2k is on AB for each value of k, and AX1 = X1X2 = X2X3 = ... = X2n-1X2n = X2nA. How many laceable acute angles, whose sizes in degrees are integers, exist?

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