
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 \( p, q, r \) be the three sides of triangle \( PQR \). If \( p^{4} + q^{4} + r^{4} = 2r^{2}(p^{2} + q^{2}) \), find \( a \), where \( a = \cos^{2} R \) and \( R \) denotes the angle opposite \( r \).

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