
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
In a triangular pyramid, the lateral faces \( DBC \) and \( DCA \) are mutually perpendicular and represent equal isosceles triangles with base \( CD = 2 \) and a side length of \( \sqrt{19} \). Find the edge \( AB \) and the areas of the pyramid's sections that are squares.

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