
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 $f(x)$ be a function defined on the set of integers. Given that $f(1) = 1$, $f(2) = 0$, $f(-1) \lt 0$, and for any integers $x$ and $y$, $f(x+y) = f(x)f(1-y) + f(1-x)f(y)$. Find $f(55)$.

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