
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
Complete the following questions as required:
1. Calculate: $(-a^{2})^{3}+9a^{4}\cdot a^{2}$;
2. Factorize: $2ab^{2}+a^{2}b+b^{3}$;
3. Calculate: $(\frac{1}{x-y}-\frac{1}{x+y})÷\frac{x-2y}{{x}^{2}-{y}^{2}}$.

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