
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

An infinite sequence of integers, \( a_0, a_1, a_2, \ldots \), with \( a_0 > 0 \), has the property that for any \( n \geq 0 \), \( a_{n+1} = a_n - b_n \), where \( b_n \) is the number having the same sign as \( a_n \), but with the digits written in reverse order. For example, if \( a_0 = 1210 \), then \( a_1 = 1089 \) and \( a_2 = -8712 \), etc. Find the smallest value of \( a_0 \) such that \( a_n \neq 0 \) for all \( n \geq 1 \).

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