
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 trihedral angle $O A B C$ has right dihedral angles. On two edges, $O A=O B=a$, while on the third edge, $O C=x$. Determine the value of $x$ such that the volume of the tetrahedron $O A B C$ is equal to $\frac{F m}{3}$, where $F$ is the surface area of the tetrahedron and $m$ is a given length. For which values of $m$ is there a solution?

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