
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 the integer part of $2+\sqrt{2}$ be denoted as $a$, and the decimal part be denoted as $b$. Similarly, let the integer part of $4-\sqrt{2}$ be denoted as $c$, and the decimal part be denoted as $d$. Find the value of $\frac{b+d}{ac}$.

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