
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 graph of \(x^{2}-(y-1)^{2}=1\) has one tangent line with positive slope that passes through \((x, y) = (0,0)\). If the point of tangency is \((a, b)\), find \(\sin^{-1}\left(\frac{a}{b}\right)\) in radians.

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