
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 $y$ be an angle such that $\tan y = \frac{p}{q}$ and $\tan 3y = \frac{q}{p + q}$. Then the least positive value of $y$ equals $\tan^{-1} m$. Compute $m$.

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