
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
َA natural number  $n$  is given. Let  $f(x,y)$  be a polynomial of degree less than  $n$  such that for any positive integers  $x,y\leq n, x+y \leq n+1$  the equality  $f(x,y)=\frac{x}{y}$  holds. Find  $f(0,0)$ .

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