
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 \( x \) be the smallest positive integer that simultaneously satisfies the following conditions: \( 2x \) is the square of an integer, \( 3x \) is the cube of an integer, and \( 5x \) is the fifth power of an integer. Find the prime factorization of \( x \).

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