
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  $x_1, x_2, ..., x_{2004}$  be a sequence of integer numbers such that  $x_{k+3}=x_{k+2}+x_{k}x_{k+1}$ ,  $\forall  1 \le k \le 2001$ . Is it possible that more than half of the elements are negative?

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