
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 using appropriate methods:<br/>$(1)3x^{2}-15=0$ (using the method of factoring)<br/>$(2)x^{2}-8x+15=0$<br/>$(3)x^{2}-6x+7=0$<br/>$(4)2x^{2}-6x+1=0$<br/>$(5)(2x^{2}+3x)^{2}-4(2x^{2}+3x)-5=0$.

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