
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
Using the digits 1, 2, 3, 4, 5, and 6, form a six-digit number \(\overline{a b c d e f}\) such that each letter represents a different digit from 1 to 6. The conditions are:
1. The two-digit number \(\overline{ab}\) is divisible by 2.
2. The three-digit number \(\overline{abc}\) is divisible by 3.
3. The four-digit number \(\overline{abcd}\) is divisible by 4.
4. The five-digit number \(\overline{abcde}\) is divisible by 5.
5. The six-digit number \(\overline{abcdef}\) is divisible by 6.

Find all such six-digit numbers and explain your reasoning process.
(Beijing, China, Middle School Math Competition, 1982)

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