
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 the medians of the triangle  $ABC$  meet at  $G$ . Let  $D$  and  $E$  be different points on the line  $BC$  such that  $DC=CE=AB$ , and let  $P$  and  $Q$  be points on the segments  $BD$  and  $BE$ , respectively, such that  $2BP=PD$  and  $2BQ=QE$ . Determine  $\angle PGQ$ .

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