
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
How many unique three-digit numbers can be formed using the digits 0, 2, 3, 4, and 6 under the following conditions:
1. The numbers must contain no repeating digits.
2. The numbers must be divisible by 3 and contain no repeating digits.
3. Calculate the sum of all positive divisors of the product 2×3×4×6 (i.e., 144). Each part of the result should be expressed numerically.

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