
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
For a real number  $a$ ,  $[a]$  denotes the largest integer not exceeding  $a$ .
Find all positive real numbers   $x$  satisfying the equation  $$ x\cdot [x]+2022=[x^2] $$  

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