
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 \( a = 0.\underbrace{00\cdots 00125}_{2013 \text{ zeroes}} \) and \( b = 0.\underbrace{00\cdots 008}_{2017 \text{ zeroes}} \), find \( a \times b + a \div b \).

The integer part of the calculation result is ______, and the decimal part is \( 0.500\cdots 01 \), where there are ______ zeroes between 5 and 1.

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