
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
Suppose a non-identically zero function  $f$  satisfies  $f\left(x\right)f\left(y\right)=f\left(\sqrt{x^2+y^2}\right)$  for all  $x$  and  $y$ . Compute   $$ f\left(1\right)-f\left(0\right)-f\left(-1\right). $$  

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