
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 fourth-degree equation  $x^4-x-504=0$  has  $4$  roots  $r_1$ ,  $r_2$ ,  $r_3$ ,  $r_4$ . If  $S_x$  denotes the value of  ${r_1}^4+{r_2}^4+{r_3}^4+{r_4}^4$ , compute  $S_4$ .

*2015 CCA Math Bonanza Individual Round #10*

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