
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
Count the number of sequences \(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\) of integers such that \(a_{i} \leq 1\) for all \(i\) and all partial sums \( (a_{1}, a_{1} + a_{2}, \ldots)\) are non-negative.

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