
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, $P = (3, -4, 4),$ $Q = (13, -14, 9),$ $R = (-3, 6, -9),$ and $S = (1, -2, 7).$ Find the intersection point of lines $PQ$ and $RS.$

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