
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 $XYZ$, $\angle Z=90^\circ$, $XZ=9$ and $ZY=12$. Points $W$ and $V$ are on $\overline{XY}$ and $\overline{YZ}$, respectively, and $\angle ZVW=90^\circ$. If $VW=6$, then what is the length of $ZW$?

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