
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
Points $K$ and $M$ lie on the sides $AB$ and $BC$ of triangle $ABC$, such that $AK: BK = 3: 2$ and $BM: MC = 3: 1$. A line $l$ is drawn through point $B$ parallel to $AC$. Line $KM$ intersects line $l$ at point $P$ and intersects line $AC$ at point $N$. Find $BP$ and $CN$ if $AC = a$.

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