
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
Find all 6-digit numbers  $a_1a_2a_3a_4a_5a_6$  formed by using the digits  $1,2,3,4,5,6$  once each such that the number  $a_1a_2a_2\ldots a_k$  is divisible by  $k$  for  $1 \leq k \leq 6$ .

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