
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
In a right triangle, one of the acute angles $\beta$ satisfies \[\tan \frac{\beta}{3} = \frac{1}{\sqrt[4]{3}}.\] Find the tangent of the angle $\phi$ between the median and the angle bisector drawn from this acute angle.

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