
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 $R$ be the set of points $(x, y)$ in the Cartesian plane that satisfy:
\[
\Big|\big| |x|-3\big|-2\Big|+\Big|\big| |y|-3\big|-2\Big|=2.
\]
Determine the total length of all the lines that make up $R$.

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