
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
On the side $AD$ of rectangle $ABCD$, a point $E$ is marked. On the segment $EC$, a point $M$ is found such that $AB = BM$ and $AE = EM$. Find the length of the side $BC$ if it is known that $ED = 16$ and $CD = 12$.

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