
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  $f_1(x)=x^2-1$ , and for each positive integer  $n \geq 2$  define  $f_n(x) = f_{n-1}(f_1(x))$ . How many distinct real roots does the polynomial  $f_{2004}$  have?

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