
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 \(ABCD\), there is a point \(E\). On segment \(EC\), there is such a point \(M\) 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}
user