
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 $P$ be a point not on line $XY$, and $Q$ a point on line $XY$ such that $PQ \perp XY$. Meanwhile, $R$ is a point on line $PY$ such that $XR \perp PY$. Given $XR = 6$, $PQ = 12$, and $XY = 7$, find the length of $PY$.

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