
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 progression \( a_{1}, a_{2}, \ldots, a_{100} \) where \( a_{3} = 9.5 \) and the common difference \( d = 0.6 \). Find the sum \( \{a_{1}\} + \{a_{2}\} + \ldots + \{a_{100}\} \). Here, \( \{x\} \) denotes the fractional part of the number \( x \), which is the difference between \( x \) and the largest integer not exceeding \( x \); for example, \( \{4.7\} = 0.7 \) and \( \left\{-5 \frac{1}{3}\right\} = \frac{2}{3} \).

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