
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
Let the sequence \(\{a_{n}\}\) have 10 terms, where \(a_{i} \in \{1, -1\}\) for \(i = 1, 2, \ldots, 10\), and for any \(k \leqslant 9\), the following conditions hold:
\[ \left|\sum_{i=1}^{k} a_{i}\right| \leq 2 \]
\[ \sum_{i=1}^{10} a_{i} = 0 \]
How many sequences \(\{a_{n}\}\) satisfy these conditions?

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