
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
Determine to how many decimal places the following approximate equality holds:

\[ 495 \sqrt{2} - 388 \sqrt{3} \approx 28 \]

In other words, how many zeros can be written after the decimal point in 28 so that the resulting number is still a rounded value of the left-hand side.

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