
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
Determine the value of the parameter \( k \) such that when the roots of the following equation are listed in ascending order, the difference between each pair of adjacent roots is the same.

$$
4 x^{4}-(4 k+13) x^{2}+(9 k+9)=0
$$


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