
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 expression:
\[
\frac{x\left(x^{2}-a^{2}\right)^{-1 / 2}+1}{a(x-a)^{-1 / 2}+(x-a)^{1 / 2}} : \frac{a^{2} \sqrt{x+a}}{x-\left(x^{2}-a^{2}\right)^{1 / 2}}+\frac{1}{x^{2}-a x}
\]

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