
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
In triangle $ABC$, suppose $AC = 360$ and $BC = 240$. Points $D$ and $E$ lie on lines $AC$ and $AB$ respectively such that $AD = DC$, and line $DE$ is the angle bisector of $\angle ADB$. Let $Q$ be the intersection of lines $BD$ and $DE$. If $AQ = 240$, find the length of $EQ$.

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