
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
There is a nine-digit number in the form $\overline{a_{1} a_{2} a_{3} b_{1} b_{2} b_{3} a_{1} a_{2} a_{3}}$ that equals the square of the product of five prime numbers, and $\overline{b_{1} b_{2} b_{3}} = 2\overline{a_{1} a_{2} a_{3}} \quad (a_{1} \neq 0)$. Find this nine-digit number.

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