
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
Determine all integers  $x$  satisfying
\[ \left[\frac{x}{2}\right] \left[\frac{x}{3}\right] \left[\frac{x}{4}\right] = x^2. \]
( $[y]$  is the largest integer which is not larger than  $y.$ )

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