
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) $(6a^4b-5a^3c^2-3a^2) \div (-3a^2)$
(2) $(2a+1)^2 - (2a+1)(-1+2a)$
(3) $|-3|+(-1)^{2011} \times (\pi-3.14)^{0}-(-\frac{1}{3})^{-2}+2^{-3}-(\frac{1}{3})^{2014} \times (-3)^{2015}$
(4) If $x^{m+2n}=16$, $x^{n}=2$, ($x \neq 0$), find the value of $x^{m+n}$
(5) Simplify and evaluate: $(2a-1)(a+2)-(2a+b)^2+2a(b-8)$, where $|a-2|+b^2+1=2b$.

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