
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 the rectangular coordinate system of a plane, the distance $d$ between a point $P(x_0, y_0)$ and a line $Ax + By + C = 0$ is given by the formula $d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}$. By applying analogous thinking, we can solve the following problem: in the rectangular coordinate system of space, find the distance $d$ between point $P(2, 1, 1)$ and the plane $3x + 4y + 12z + 4 = 0$. That is, $d =$ \_\_\_\_\_\_.

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