
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
A function \( h \) is defined recursively by \( h(1)=2 \), \( h(2)=3 \), and 
\[ h(n)=h(n-1)-h(n-2)+2n \] 
for all integers \( n \geq 3 \). Find \( h(2023) \).

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