
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 real number \( y \) satisfies the equation \( y + \frac{1}{y} = 3 \). What is the value of \( y^{13} - 5y^9 + y^5 \)?
A) -46206
B) 121041
C) 0
D) 121041y - 46206
E) -1

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