
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 that the sequence $\{a_{n}\}$ is an arithmetic sequence, with the sum of its first $n$ terms denoted as $S_{n}$, $a_{1}=-19$, $a_{7}-a_{4}=6$. If for any $n\in N^{*}$, $S_{n}\geqslant S_{m}$ always holds, determine the value of $m$.

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