
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
Find the derivative \( y_{x}^{\prime} \).

$$
\left\{\begin{array}{l}
x=\sqrt{t-t^{2}}-\operatorname{arctg} \sqrt{\frac{1-t}{t}} \\
y=\sqrt{t}-\sqrt{1-t} \cdot \arcsin \sqrt{t}
\end{array}\right.
$$

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