
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 the functions $f(x) = x^3 + ax$ and $g(x) = bx^2 + c$, their graphs intersect at point $P(t, 0)$, and $t \neq 0$. The graphs of the two functions have the same tangent line at point $P$.  
(1) When $t=1$, find $a$, $b$, $c$.  
(2) If the function $y = g(x) - f(x)$ is monotonically increasing in the interval $(-1, 3)$, find the range of values for $t$.

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