
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
Let  $r$  be a positive real number. Denote by  $[r]$  the integer part of  $r$  and by  $\{r\}$  the fractional part of  $r$ . For example, if  $r=32.86$ , then  $\{r\}=0.86$  and  $[r]=32$ . What is the sum of all positive numbers  $r$  satisfying  $25\{r\}+[r]=125$ ?

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