
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 a right triangle $ABC$ with $AB=13$, $BC=5$ and $AC=12$, a circle with center $Q$ is tangent to side $BC$ at $B$ and passes through point $A$, and another circle with center $R$ is tangent to side $AC$ at $A$ and passes through point $B$, find the distance between $Q$ and $R$.

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