
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  $P(x)=x^2+bx+c$ . Suppose  $P(P(1))=P(P(-2))=0$  and  $P(1)\neq P(-2)$ . Then  $P(0)=$ [list=1]
[*]  $-\frac{5}{2}$ [*]  $-\frac{3}{2}$ [*]  $-\frac{7}{4}$ [*]  $\frac{6}{7}$ [/list]

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