
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 trapezoid \(ABCD\) is given. On its side \(CD\), a point \(M\) is chosen such that \( \frac{CM}{MD} = \frac{4}{3} \). It is found that the segment \(BM\) divides diagonal \(AC\) into two segments with a ratio of lengths also equal to \( \frac{4}{3} \). What values can the ratio \( \frac{AD}{BC} \) take? If necessary, round the answer to 0.01 or write the answer as a simple fraction.

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