
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
 $a_1a_2a_3$  and  $a_3a_2a_1$  are two three-digit decimal numbers, with  $a_1$  and  $a_3$  different non-zero digits. Squares of these numbers are five-digit numbers  $b_1b_2b_3b_4b_5$  and  $b_5b_4b_3b_2b_1$  respectively. Find all such three-digit numbers.

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