
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  $A, B, C$  be unique collinear points $ AB = BC =\frac13$ . Let  $P$  be a point that lies on the circle centered at  $B$  with radius  $\frac13$  and the circle centered at  $C$  with radius  $\frac13$  . Find the measure of angle  $\angle PAC$  in degrees.

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