
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 expressions:

\[
\begin{gathered}
\frac{\sqrt{a}+\sqrt{b}-\sqrt{a-b}}{\sqrt{a}+\sqrt{b}+\sqrt{a-b}} \\
\frac{\sqrt{a}-\sqrt{a-1}-\sqrt{a^{2}-a}+\sqrt{a+2-a-1}}{\sqrt{a^{2}-a}+\sqrt{a^{2}-a-1}-\sqrt{a}-\sqrt{a-1}}
\end{gathered}
\]

Calculate the value of (2) to three significant digits when \( a=3 \) and \( a=4 \).

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