
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 \(1, 2, 3, \ldots, 29, 30\) are written in a row in a random order, and their partial sums are calculated: the first sum \(S_1\) is equal to the first number, the second sum \(S_2\) is equal to the sum of the first and second numbers, \(S_3\) is equal to the sum of the first, second, and third numbers, and so on. The last sum \(S_{30}\) is equal to the sum of all the numbers. What is the highest possible count of odd numbers among the sums \(S_{1}, S_{2}, \ldots, S_{30}\)?

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