
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 side \(AD\) of rectangle \(ABCD\) a point \(E\) is marked. On segment \(EC\) there is a point \(M\) such that \(AB = BM\) and \(AE = EM\). Find the length of side \(BC\), given that \(ED = 16\) and \(CD = 12\).

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