
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. 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 that \(\cos \alpha' = \frac{2}{5}\) and \(\cos \beta' = \frac{1}{4}\), and that \(OQ^2 = 53\), determine \(\cos \gamma'\).

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