
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 $1, 2, 3, 4, 5, 6$, form a six-digit number $\overline{abcdef}$, where different letters represent different digits from $1$ to $6$. The number must satisfy the following conditions:
- The two-digit number $\overline{ab}$ is a multiple of $2$.
- The three-digit number $\overline{abc}$ is a multiple of $3$.
- The four-digit number $\overline{abcd}$ is a multiple of $4$.
- The five-digit number $\overline{abcde}$ is a multiple of $5$.
- The six-digit number $\overline{abcdef}$ is a multiple of $6$.

Find all such six-digit numbers and explain your reasoning process.

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