
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 the isosceles trapezoid \(ABCD\), the base \(AD\) is equal to 4, and the base \(BC\) is equal to 3. Points \(M\) and \(N\) lie on the diagonal \(BD\), with point \(M\) located between points \(B\) and \(N\), and the segments \(AM\) and \(CN\) perpendicular to the diagonal \(BD\). Find \(CN\) if \(BM:DN = 2:3\).

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