
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
Elisenda has a piece of paper in the shape of a triangle with vertices \(A, B\), and \(C\) such that \(AB = 42\). She chooses a point \(D\) on segment \(AC\), and she folds the paper along line \(BD\) so that \(A\) lands at a point \(E\) on segment \(BC\). Then, she folds the paper along line \(DE\). When she does this, \(B\) lands at the midpoint of segment \(DC\). Compute the perimeter of the original unfolded triangle.

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