
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 the greatest integer $n$ such that $n \leq x$. For example, $[10] = 10$, $[9.93] = 9$, $\left[\frac{1}{9}\right] = 0$, $[-1.7] = -2$. Find all solutions to the equation $\left[\frac{x+3}{2}\right]^{2} - x = 1$.

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