
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 a coordinate space, consider a point $Q$ where the $x$ coordinate is negative and the $y$ and $z$ coordinates are positive. The line between the origin and $Q$ is drawn. The angles between this line and the $x$-, $y$-, and $z$-axis are $\alpha$, $\beta$, and $\gamma$ respectively. Given $\cos \alpha = -\frac{1}{4}$ and $\cos \beta = \frac{1}{2}$, determine $\cos \gamma$.

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