
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 sequence of real numbers  $\{a_n\}$ ,  $n \in \mathbb{N}$  satisfies the following condition:  $a_{n+1}=a_n(a_n+2)$  for any  $n \in \mathbb{N}$ . Find all possible values for  $a_{2004}$ .

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