
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 \( a_{1}, a_{2}, \ldots, a_{R} \) be positive integers such that \( a_{1} < a_{2} < a_{3} < \ldots < a_{R-1} < a_{R} \). Given that the sum of these \( R \) integers is 90 and the maximum value of \( a_{1} \) is \( S \), find the value of \( S \).

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