
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
A circle $\Gamma$ with center $I$ is inscribed in a right triangle $ABC$ with $\angle B = 90^\circ$. The circle touches sides $AB$ and $BC$ at points $K$ and $L$ respectively. A line passing through point $I$ intersects sides $AB$ and $BC$ at points $M$ and $N$ respectively. The radius of circle $\Gamma$ is to be found given that $MK = 144$ and $NL = 25$. Find $AC$ if it is additionally known that line $MN$ is parallel to $AC$.

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