
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 and determine which statement is true for all solutions:
1. $2x^2 - 4 = 36$
2. $(3x-2)^2 = (x+2)^2$
3. $\sqrt{3x^2 - 10} = \sqrt{2x + 2}$
A) All equations have integral roots
B) No root greater than 3
C) At least one root is zero
D) Only one root per equation
E) Each equation has one negative and one positive root

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