
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
Consider the set \( T \) of all points \( (x, y) \) in the Cartesian plane that satisfy the equation:
\[ \Big| \big| |x| - 3 \big| - 2 \Big| + \Big| \big| |y| - 3 \big| - 2 \Big| = 2. \]

What is the total length of all the lines that make up set \( T \)?

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