
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
Given a nine-digit number of the form $\overline{a_{1} a_{2} a_{3} b_{1} b_{2} b_{3} a_{1} a_{2} a_{3}}$, which is equal to the square of the product of five different prime numbers, and where $\overline{b_{1} b_{2} b_{3}} = 2 \cdot \overline{a_{1} a_{2} a_{3}}$, find this nine-digit number.

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