
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 questions:
1. Given that $\sqrt{a^3+8}$ and $|b^{2}-9|$ are opposite in sign, $ab \lt 0$, find the value of $\left(b-a\right)^{a}$.
2. Given that the square root of a certain positive number is $1-2a$ and $3a-4$, find this positive number.

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