
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 $h$ such that $h(1) = 3$, $h(2) = 2$, and for all integers $n \geq 3$, 
\[ h(n) = 2h(n-1) - h(n-2) + 2n + 1. \]
Determine the value of $h(10)$.

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