
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  $ABC$  be a triangle, and let  $P$  be a point on side  $BC$  such that  $\frac{BP}{PC}=\frac{1}{2}$ . If  $\measuredangle ABC$   $=$   $45^{\circ}$  and  $\measuredangle APC$   $=$   $60^{\circ}$ , determine  $\measuredangle ACB$  without trigonometry.

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