
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 $\{a_n\}$ with the first term $a_1=m$, and the sum of its first $n$ terms is $S_n$, satisfying $S_n+S_{n+1}=3n^2+2n$. If for $\forall n \in \mathbb{N}_+$, $a_n < a_{n+1}$ always holds, then the range of $m$ is \_\_\_\_\_\_.

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