
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
Justin the robot is on a mission to rescue abandoned treasure from a minefield.  To do this, he must travel from the point  $(0, 0, 0)$  to  $(4, 4, 4)$  in three-dimensional space, only taking one-unit steps in the positive  $x, y,$  or  $z$ -directions.  However, the evil David anticipated Justin's arrival, and so he has surreptitiously placed a mine at the point  $(2,2,2)$ .  If at any point Justin is at most one unit away from this mine (in any direction), the mine detects his presence and explodes, thwarting Justin.

How many paths can Justin take to reach his destination safely?

*Proposed by Justin Stevens*

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