
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 quartic (4th-degree) polynomial P(x) satisﬁes  $P(1)=0$  and attains its maximum value of  $3$  at both  $x=2$  and  $x=3$ . Compute  $P(5)$ .

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