
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
Below is the graph of $y = a \tan (b(x - c))$ for some positive constants $a$, $b$, and a phase shift $c$. The graph has a period of $\frac{\pi}{4}$, passes through the point $\left(\frac{\pi}{3}, -4\right)$, and has a vertical asymptote at $x = \frac{\pi}{4}$. Find the value of $4ab$.

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