
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
$PQRS$ is a regular tetrahedron (equilateral triangular pyramid). If $N$ is the midpoint of $\overline{QR}$, calculate $\cos \angle PNS$, where $S$ is the vertex opposite base $PQR$.

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