
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
The numbers from 1 to 10 were written in some order, resulting in the numbers \( a_{1}, a_{2}, a_{3}, \ldots, a_{10} \). Then the sums \( S_{1} = a_{1} \), \( S_{2} = a_{1} + a_{2} \), \( S_{3} = a_{1} + a_{2} + a_{3} \), \(\ldots\), \( S_{10} = a_{1} + a_{2} + a_{3} + \ldots + a_{10} \) were calculated. What is the maximum number of prime numbers that could appear among the numbers \( S_{1}, S_{2}, S_{3}, \ldots, S_{10} \)?

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