
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
(1) Solve for $x$ in the following equations:  
① $(x-1)^3 = -8$;  
② $(x+1)^2 = 25$.  
(2) Given that the square roots of a certain number are $a+3$ and $2a-15$, and the cube root of $b$ is 2, find the square root of $b-a$.

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