
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
Given a convex pentagon $ABCDE$, point $P$ is the intersection of $BE$ and $AC$, point $Q$ is the intersection of $CE$ and $AD$, point $O$ is the intersection of $AD$ and $BE$. It turned out that $ABP$ and $DEQ$ are isosceles triangles with an apex angle (specifically at the apex, not the base) equal to 80 degrees. Find the measure of angle $ACE$, given that triangles $APO$ and $EQO$ are also isosceles.

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