
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
On the number line, points with coordinates 1, 2, ..., 2006 are called marked points. A frog starts from point 1, makes 2006 jumps, goes through all the marked points, and returns to the starting point. What is the maximum total length of all the paths the frog has jumped? Explain your reasoning.

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