
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
For variables $x$ and $y$ satisfying the system of equations
$$
\begin{cases} 
x = \sqrt{t}, \\
y = 2\sqrt{1-t},
\end{cases}
$$
where $t$ is a parameter, find the range of values for the algebraic expression $\frac{y+2}{x+2}$.

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