
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 the general term of an arithmetic sequence $\{a_{n}\}$ is $a_{n}=2n-1$, and the sum of its first $n$ terms is denoted as $S_{n}$, if $S_{m}$ is the arithmetic mean of $a_{m}$ and $a_{m+1}$, find the value of $m$.

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