
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
The base of the pyramid \(ABCD\) is an isosceles right triangle \(ABC\) with hypotenuse \(AB = 4\). The height of the pyramid is 2, and its apex is located at the midpoint of \(AC\). Find the dihedral angle between the faces \(ABD\) and \(ADC\).

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