
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
Solve the equation:
\[ [x] \times \{x\} + x = 2\{x\} + 9 \]
where \([x]\) denotes the integer part of \(x\) and \(\{x\}\) denotes the fractional part of \(x\). For example, if \(x = 3.14\), then \([3.14] = 3\) and \(\{3.14\} = 0.14\). (Find all solutions).

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