
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 $x$ and $y$ be angles such that $\tan x = \frac{a}{b}$, and $\tan (x+y) = \frac{b}{a+b}$ where $y = x$. Compute the least positive value of $x$ in terms of $a$ and $b$, where $x = \tan^{-1} k$.

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