
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
Solve the puzzle UHA = LCM(UH, UA, HA). Here, U, H, and A are three distinct digits. Two-digit and three-digit numbers cannot start with zero. Recall that the LCM of several natural numbers is the smallest natural number that is divisible by each of them.

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