
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's consider the following expression:

\[ 
E(x) = \sin^6 x + \cos^6 x + p(\sin^4 x + \cos^4 x) 
\]

a) Determine the value of the parameter \( p \) such that the value of the expression is independent of \( x \).

b) For which values of \( p \) does the equation \( E(x) = 0 \) have (real) solutions?

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