
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
Let $\triangle ABC$ be a triangle in the plane, and let $D$ be a point outside of the plane of $\triangle ABC$, thereby forming a pyramid $DABC$ with all triangular faces.
Suppose that the length of every edge in $DABC$ is either $13$ or $34$, with the condition that no face of $DABC$ is an equilateral triangle. Determine the surface area of pyramid $DABC$.

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