
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
For some  $ p$ , the equation  $ x^3 \plus{} px^2 \plus{} 3x \minus{} 10 \equal{} 0$  has three real solutions  $ a,b,c$  such that  $ c \minus{} b \equal{} b \minus{} a > 0$ . Determine  $ a,b,c,$  and  $ p$ .

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