
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
Let \( x \) be a positive integer, and write \( a = \left\lfloor \log_{10} x \right\rfloor \) and \( b = \left\lfloor \log_{10} \frac{100}{x} \right\rfloor \). Here \( \lfloor c \rfloor \) denotes the greatest integer less than or equal to \( c \). Find the largest possible value of \( 2a^2 - 3b^2 \).

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