
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 ends of segment \( AB \) belong to the faces of the dihedral angle equal to \( \phi \). The distances \( AA_1 \) and \( BB_1 \) from points \( A \) and \( B \) to the edge of the dihedral angle are \( a \) and \( b \) respectively, and \( A_1 B_1 = c \). Find \( AB \).

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