
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 $T$ be the set of points $(x, y)$ in the Cartesian plane that satisfy
\[
\left| \left| |x| - 3 \right| - 2 \right| + \left| \left| |y| - 3 \right| - 2 \right| = 2.
\]
What is the total length of all lines that make up $T$?

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