
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
Let triangle $ABC$ be a right triangle with right angle at $C$. Let $F$ and $G$ be points on $\overline{AB}$ such that $\overline{CF}$ and $\overline{CG}$ trisect $\angle C$. If $\frac{FG}{BG} = \frac{3}{7}$, find $\tan B$.

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