
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 equations:
1) \(\frac{x^{2}-3 x}{\sqrt{x-3}}=0\);
2) \(x^{2}-6|x|+9=0\);
3) \((x-1)^{4}=4\);
4) \(\left[x^{2}\right]+x=6\);
5) \(x^{2}+x=0\) or \(x^{2}-1=0\);
6) \(x^{2}-2 x-3=0\) and \(|x|<2\).

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