
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
Given \(0 < x < \frac{\pi}{2}\) and \(\sin x - \cos x = \frac{\pi}{4}\), if \(\tan x + \frac{1}{\tan x}\) can be expressed in the form \(\frac{a}{b - \pi^c}\) where \(a\), \(b\), and \(c\) are positive integers, then find the value of \(a + b + c\).

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