
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  $P$  be a polynomial with real coefficients. Find all functions  $f : \mathbb{R} \rightarrow \mathbb{R}$  such that there exists a real number  $t$  such that
\[f(x+t) - f(x) = P(x)\]
for all  $x \in \mathbb{R}$ .

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