
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
The remainders when the polynomial \( p(x) \) is divided by \( (x+1) \) and \( (x-1) \) are 7 and 5, respectively. Find the sum of the coefficients of the odd powers of \( x \). 
(a) -4 
(b) 2 
(c) -1 
(d) 12

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