
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
Given a sequence $\{a_{n}\}$ where $a_{1}=1$, $a_{2}=2$, and $a_{n+2}-a_{n}=\left(-1\right)^{n}+2$, find the sum of the first $30$ terms of the sequence $\{a_{n}\}$.

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