
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
The sequences $\{a_n\}$ and $\{b_n\}$ satisfy the equation $b_{n}=a_{n+1}+(-1)^{n}a_{n}$ for all $n\in\mathbb{N}^*$, and the sum of the first $n$ terms of the sequence $\{b_n\}$ is $n^2$. Given that the sum of the first 2018 terms of the sequence $\{a_n-n\}$ is 1, find the first term $a_1$ of the sequence $\{a_n\}$.

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