
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
Given that the function f(x) = -(a+2)x² + (k-1)x - a, with a domain of [a-2, a+4], is an even function,

1. Find the values of a and k, and write out the monotonically decreasing interval of the function y = |f(x)|.
2. Solve the inequality f(t-1) - f(t) > 0 with respect to t.

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