
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  $P(x)$  be the polynomial of degree at most  $6$  which satisfies  $P(k)=k!$  for  $k=0,1,2,3,4,5,6$ . Compute the value of  $P(7)$ .

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