
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 function \( h \) be defined recursively with initial conditions \( h(1) = 2, h(2) = 2 \), and for all \( n \geq 3 \), the recursive relationship is defined as:
\[
h(n) = h(n-1) - h(n-2) + n + \sin\left(\frac{n\pi}{6}\right).
\]
Calculate \( h(2030) \).

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