
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 two lines with a slope of $k (k \neq 0)$ intersect the graph of the function $f(x) = x^3 + (t - 1)x^2 - 1$ at points $A$ and $B$, and the equation of line $AB$ is $y = 2x - 1$, determine the value of $t + k$.

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