
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
(1) Convert the parametric equations 
\[
\begin{cases}
x=3+4\cos \theta \\
y=-2+4\sin \theta
\end{cases} 
\]
(where $\theta$ is the parameter) into a Cartesian equation.

(2) Given 
\[
(2x+ \sqrt{3})^{4}=a_0+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4},
\]
find the value of 
\[
(a_{0}+a_{2}+a_{4})^{2}-(a_{1}+a_{3})^{2}.
\]

(3) If the function $f(x)=kx-\ln x$ is monotonically increasing on the interval $(1,+\infty)$, then the range of values for $k$ is _______.

(4) During the Spring Festival, Xiao Ming and his parents played a game of grabbing red envelopes. His father released 12 red envelopes in sequence with amounts from 1 yuan to 12 yuan, each time releasing one. All three grabbed at the same time, and in the end, each person grabbed 4 red envelopes. His father said: I grabbed 1 yuan and 3 yuan; his mother said: I grabbed 8 yuan and 9 yuan; Xiao Ming said: The sum of the amounts each of us grabbed is equal. Based on this, it can be determined that the two amounts Xiao Ming definitely grabbed are _______.

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