
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
A rectangular shape \( ABCD \) with sides \( a \) and \( b \) is folded along the diagonal \( BD \) so that the planes of triangles \( BAD \) and \( BCD \) become mutually perpendicular. Find \( AC \).

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