
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
Joe and Gracie are at positions $3+4i$ and $-2+3i$ respectively on the complex plane. A third point, $1+i$, is also marked on the plane. Calculate the total distance Joe travels if he first moves directly to the third point and then directly to Gracie's position.

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