
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
Define a function $f$ recursively by $f(1) = 1$, $f(2) = 2$, and
\[ f(n) = 2f(n-1) - f(n-2) + n^2 \]
for all integers $n \geq 3$. What is $f(10)$?

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