
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 triangle $XYZ$ be a right triangle with right angle at $Z$. Let $P$ and $Q$ be points on $\overline{XY}$ with $P$ between $X$ and $Q$ such that $\overline{ZP}$ and $\overline{ZQ}$ trisect $\angle Z$. If $\frac{PQ}{QY} = \frac{3}{7}$, find $\tan Y$.

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