
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 numbers \( N = \overline{a_{1} a_{2} \ldots a_{n}} \) for which \( 9 \times \overline{a_{1} a_{2} \ldots a_{n}} = \overline{a_{n} \ldots a_{2} a_{1}} \), such that at most one of the digits \( a_{1}, a_{2}, \ldots, a_{n} \) is zero.

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