
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
Find all \( x \) for which \( [x] + \{ 2x \} = 2.5 \), where \( [x] \) denotes the integer part of \( x \), and \( \{ x \} \) denotes the fractional part of \( x \), that is, \( \{ x \} = x - [x] \).

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