
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 an arithmetic sequence ${a_n}$ with the sum of its first $n$ terms denoted as $S_n$, and given that $S_{m-1}=16$, $S_m=25$, $S_{m+2}=49$ ($m\geq 2$ and $m\in\mathbb{N}$), determine the value of $m$.

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