
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 function \( f \) is given by the table

| \(x\) | 1 | 2 | 3 | 4 | 5 |
| :---: | :--- | :--- | :--- | :--- | :--- |
| \( f(x) \) | 4 | 1 | 3 | 5 | 2 |

For example, \( f(2)=1 \) and \( f(4)=5 \). What is the value of \( \underbrace{f(f(f(f(\ldots f}_{2004 \text{ times }}(4) \ldots))) \)? 
(a) 1  
(b) 2  
(c) 3  
(d) 4  
(e) 5

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