
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 a common difference of -2, the sum of its first $n$ terms is $S_n$, and $a_3$, $a_4$, $a_5$ are the side lengths of a triangle with one of its internal angles being 120°. If $S_n \leq S_m$ holds true for any $n \in \mathbb{N}^+$, determine the real number $m$.

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