
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 \(ABC\), a point \(D\) is marked on side \(BC\) such that \(BD: DC = 1:3\). Additionally, points \(E\) and \(K\) are marked on side \(AC\) such that \(E\) lies between \(A\) and \(K\). Segment \(AD\) intersects segments \(BE\) and \(BK\) at points \(M\) and \(N\) respectively, and it is given that \(BM: ME = 7:5\) and \(BN: NK = 2:3\). Find the ratio \(MN: AD\).

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