
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
Simplify the following fractions:

$$
\begin{array}{ll}
\text { 1. } \frac{a \sqrt{x}-x \sqrt{a}}{\sqrt{a}-\sqrt{x}} & \text { 2. } \frac{\sqrt{a+b}-\sqrt{a-b}}{a+b-\sqrt{a^{2}-b^{2}}}
\end{array}
$$

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