
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 $f$ as follows: $f(1)=2$, $f(2)=3$, and for all integers $n \geq 3$,
\[f(n)=f(n-1)+f(n-2)+(2n).\]
Calculate $f(10)$.

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