
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
Define  $\lfloor x \rfloor$  as the largest integer less than or equal to  $x$ . Define  $\{x \} = x - \lfloor x \rfloor$ . For example,  $\{ 3 \} = 3-3 = 0$ ,  $\{ \pi \} = \pi - 3$ , and  $\{ - \pi \} = 4-\pi$ . If  $\{n\} + \{ 3n\} = 1.4$ , then find the sum of all possible values of  $100\{n\}$ .

*Proposed by Isabella Grabski*

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