
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 function $f(x)=-\cos ^{2}x-4t\cdot\sin \frac {x}{2}\cos \frac {x}{2}+2t^{2}-6t+2 (x\in R)$, where $t\in R$, let $g(t)$ denote the minimum value of $f(x)$.
(1) Find the expression for $g(t)$;
(2) When $-1 < t < 1$, find the range of the real number $k$ such that the equation $g(t)=kt$ has exactly one real root.

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