
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 problem using the maximum number of different methods. Different methods are considered to be those employing different mathematical ideas, as well as different technical approaches to implementing the same idea. Specify the place of each method used in the school mathematics course.

Determine (depending on the value of parameter \(a\)) the number of solutions of the equation \(\sqrt{x}+\sqrt{6-2x}=a\).

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