
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  $f(x)=\tfrac{x+a}{x+b}$  for real numbers  $x$  such that  $x\neq -b$ . Compute all pairs of real numbers  $(a,b)$  such that  $f(f(x))=-\tfrac{1}{x}$  for  $x\neq0$ .

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