
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 $ABC$, $AB=125$, $AC=130$ and $BC=120$. The angle bisectors of angles $A$ and $B$ intersect $\overline{BC}$ and $\overline{AC}$ at points $L$ and $K$, respectively. $C$ projects onto $\overline{AL}$ at $N$ and onto $\overline{BK}$ at $M$. Find the length of $MN$.

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