
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 first term $a$ and common difference $-4$. Let $S\_n$ be the sum of its first $n$ terms. If there exists an $m \in \mathbb{N}^+$ such that $S\_m = 36$, find the minimum value of the real number $a$.

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