
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
If the function $y = f(x)$ has an inverse function $y = f^{-1}(x)$, and the graph of the function $y = \tan\left(\frac{\pi x}{6}\right) - f(x)$ passes through the point $(2, \sqrt{3} - \frac{1}{3})$, then the graph of the function $y = f^{-1}(x) - \frac{\pi}{2}$ must pass through which point?

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