
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
In coordinate space, a particle starts at the point $(1,2,3)$ and ends at the point $(-2,-2, -4)$, traversing the line connecting these points. Along this path, the particle intersects with a sphere with radius 2 centered at the point $(1,1,1)$. Calculate the distance between the two points where the particle intersects the sphere.

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