
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
Find all real roots of the quartic \( x^4 - (2N + 1)x^2 - x + N^2 + N - 1 = 0 \) correct to 4 decimal places, where \( N = 10^{10} \).

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