
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 sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, and $a\_1 = -10, a_{n+1} = a\_n + 3 (n \in \mathbb{N}^*)$, determine the value of $n$ when $S\_n$ reaches its minimum.

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