
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
Consider $\triangle ABC$ with $\angle A = 60^\circ$, $\angle B = 50^\circ$, and $\angle C = 70^\circ$. $ABCDE$ is a pentagon where each vertex lies on the midpoint of each side of $\triangle ABC$, such that $D$ is on $\overline{AB}$, $E$ is on $\overline{BC}$, and each side of the pentagon is tangent to a common circle, which is also circumscribed around $ABCDE$. Calculate the measure of $\angle ADE$.

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