
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
The integer part \([x]\) of a number \(x\) is defined as the largest integer \(n\) such that \(n \leqslant x\), for example, \([10]=10\), \([9.93]=9\), \(\left[\frac{1}{9}\right]=0\), \([-1.7]=-2\). Find all solutions to the equation \(\left[\frac{x-1}{2}\right]^{2} + 2x + 2 = 0\).

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