
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
Given an arithmetic sequence \\( \{a_n\} \\) with the sum of the first \\( n \\) terms denoted as \\( S_n \\), it is known that \\( S_{17} < 0 \\) and \\( S_{18} > 0 \\). Determine the value of \\( n \\) for the smallest term in \\( S_n \\).

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