
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 distance $A_{1} H$ from point $A_{1}(1, 6, -7)$ to the plane $A B_{1} K$ defined by the points $A(-1, 2, -3)$, $B_{1}(5, 8, -3)$, and $K(-1, 8, -6)$.

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