
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
Can all roots of the equations \( x^{2} - px + q = 0 \) and \( x^{2} - (p+1)x + q = 0 \) be integers if:
a) \( q > 0 \)

b) \( q < 0 \) ?

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