
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
Starting from a positive integer \( a \), we formed the numbers \( b = 2a^2 \), \( c = 2b^2 \), and \( d = 2c^2 \). What could the number \( a \) have been if the decimal representations of \( a \), \( b \), and \( c \) written consecutively in this order form exactly the decimal representation of \( d \)?

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