
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
Find the point of intersection of the line passing through the vertices $A_4$ and the face $A_1A_2A_3$.

$A_1(1, 2, -3)$

$A_2(1, 0, 1)$

$A_3(-2, -1, 6)$

$A_4(0, -5, -4)$

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