
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 three-dimensional coordinate space, consider a point $P = (x, y, z)$ in which $x, y, z > 0$. A line is drawn from the origin to point $P$. The angle between this line and the x-axis is $\alpha$, with the y-axis is $\beta$, and the z-axis is $\gamma$. Given $\cos \alpha = \frac{1}{4}$ and $\cos \beta = \frac{1}{3}$, find $\cos \gamma$.

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