
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
Each positive integer \(\alpha\) undergoes the following procedure to obtain the number \(d = d(a)\):
1. Move the last digit of \(a\) to the first position to obtain the number \(b\).
2. Square \(b\) to obtain the number \(c\).
3. Move the first digit of \(c\) to the end to obtain the number \(d\).

For example, for \( a = 2003 \):
- \( b = 3200 \)
- \( c = 10240000 \)
- \( d = 02400001 = 2400001 = d(2003) \)

Find all numbers \(a\) for which \( d(a) = a^2 \).

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