
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 \( a_n = 1 + 2 + \cdots + n \) where \( n \in \mathbf{Z}_{+} \), and
\[ S_m = a_1 + a_2 + \cdots + a_m \text{ for } m = 1, 2, \cdots, \]
find the number of terms among \( S_1, S_2, \cdots, S_{2017} \) that are divisible by 2 but not by 4.

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