
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
Solve the following equation for \( x \):

$$
\sqrt{\log _{a} \sqrt[4]{a x}+\log _{x} \sqrt[4]{a x}}+\sqrt{\log _{a} \sqrt[4]{\frac{x}{a}}+\log _{x} \sqrt[4]{\frac{a}{x}}}=a
$$

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