
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 vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with $|\overrightarrow{a}|=|\overrightarrow{b}|=1$ and $|\overrightarrow{a}+k\overrightarrow{b}|=\sqrt{3}|k\overrightarrow{a}-\overrightarrow{b}|$ where $k > 0$, let $f(k)=\overrightarrow{a} \cdot \overrightarrow{b}$.  
(1) Express $f(k)$ in terms of $k$.  
(2) When $k > 0$, find the range of values for the real number $x$ such that $f(k)\geq x^{2}-2tx- \frac{5}{2}$ holds true for any $t$ in the interval $[-2,2]$.

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