
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
Point \(Q\) is located inside triangle \(DEF\) such that angles \(QDE\), \(QEF\), and \(QFD\) are all congruent. The sides of the triangle have lengths \(DE=12\), \(EF=13\), and \(FD=15\). Find \(\tan \angle QDE\).

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