
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 a sequence $\{a\_n\}$ that satisfies $a\_n = a\_{n-1} - a\_{n-2}$ for $n \geq 3, n \in \mathbb{N}^*$, and its sum of the first $n$ terms is $S\_n$. If $S\_9 = 6$ and $S\_{10} = 5$, find the value of $a\_1$.

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