
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, $A = (3,-5,4),$ $B = (13,-15,9),$ $C = (-6,6,-12),$ and $D = (-4,-2,8).$ Find the intersection point of lines $AB$ and $CD.$

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