
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's call a number \( x \) semi-integer if the number \( 2x \) is an integer. The semi-integer part of a number \( x \) is the largest semi-integer number that does not exceed \( x \), and we denote it as \( ]x[\right. \). Solve the equation \( x^2 + 2 \cdot ]x[ = 6 \). (20 points)

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