
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
Given that the structure of a methane molecule $\mathrm{CH}_{4}$ consists of a central carbon atom surrounded by 4 hydrogen atoms (these four hydrogen atoms form the four vertices of a regular tetrahedron), let $\theta$ be the angle between any two of the four line segments connecting the central carbon atom to the four hydrogen atoms. Determine $\cos \theta$.

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