
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
Let $Q$ be a point in coordinate space where all coordinates of $Q$ are positive. A line is drawn from the origin to $Q$. The angles between this line and the $x$-, $y$-, and $z$-axis are $\alpha'$, $\beta'$, and $\gamma'$, respectively. Given that $\cos \alpha' = \frac{1}{4}$ and $\cos \beta' = \frac{1}{2}$, find $\cos \gamma'$.

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