
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
On the edge of a dihedral angle of $120^{\circ}$, a segment of length $c$ is taken, and from its ends, perpendiculars to it are drawn, lying in different faces of the given dihedral angle and having lengths $a$ and $b$. Find the length of the segment of the line connecting the ends of these perpendiculars.

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