
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 \( x \) such that \( 2[x] + \{3x\} = \frac{7}{3} \), where \( [x] \) is the integer part of \( x \) and \( \{x\} \) is the fractional part of \( x \) (i.e., \( \{x\} = x - [x] \)).

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