
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 the sum of the first $n$ terms is $S_n$ ($n \in \mathbb{N}^*$), and it satisfies $S_n + S_{n+1} = 2n^2 + n$. If for every $n \in \mathbb{N}^*$, $a_n < a_{n+1}$ always holds, then the range of values for the first term $a_1$ is ______.

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