
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
Given a trapezoid \( ABCD \). On its lateral side \( CD \), a point \( M \) is chosen such that \( \frac{CM}{MD} = \frac{4}{3} \). It turns out that the segment \( BM \) divides the diagonal \( AC \) into two segments whose lengths are also in the ratio \( \frac{4}{3} \). What values can the ratio \( \frac{AD}{BC} \) take? If necessary, round the answer to 0.01 or write the answer in the form of a common fraction.

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