
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
We call a decimal number balanced if the sum of the digits before the decimal point is equal to the sum of the digits after the decimal point. For example, the number 25.133 is balanced. In each of the numbers 497365.198043 and 197352.598062, strike out some digits to create:
a) the largest possible balanced number,
b) a balanced number with the maximum number of digits.

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