
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  $S$  be the set of all real values of  $x$  with  $0 < x < \pi/2$  such that  $\sin x$ ,  $\cos x$ , and  $\tan x$  form the side lengths (in some order) of a right triangle.  Compute the sum of  $\tan^2 x$  over all  $x$  in  $S$ .

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