
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 with all positive coordinates. A line from the origin to \( Q \) forms angles \( \alpha', \beta', \) and \( \gamma' \) with the \( x \)-, \( y \)-, and \( z \)-axis respectively. Given \( \cos \alpha' = \frac{2}{5} \) and \( \cos \beta' = \frac{1}{4}, \) find \( \cos \gamma' \).

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