
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 $XYZ$, the sides are $XY=13, YZ=14,$ and $XZ=15.$ Circle $\phi_1$ passes through $Y$ and is tangent to line $XZ$ at $Z.$ Circle $\phi_2$ passes through $X$ and is tangent to line $YZ$ at $Z.$ Let $P$ be the intersection of circles $\phi_1$ and $\phi_2$ not equal to $Z.$ Find the length of $ZP$ in simplest fractional form.

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