
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
$O A B C$ is a tetrahedron with $O A, O B$ and $O C$ being mutually perpendicular. Given that $O A = O B = O C = 6x$.

1. If the volume of $O A B C$ is $a x^{3}$, find $a$.
2. If the area of $\triangle A B C$ is $b \sqrt{3} x^{2}$, find $b$.
3. If the distance from $O$ to $\triangle A B C$ is $c \sqrt{3} x$, find $c$.
4. If $\theta$ is the angle of depression from $C$ to the midpoint of $A B$ and $\sin \theta = \frac{\sqrt{d}}{3}$, find $d$.

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