
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
$$
\frac{2(a+(a+1)+(a+2)+\ldots+2a)}{a^{2}+3a+2}+\frac{6\left(a^{1/2}+b^{1/2}\right)}{(a-b)^{0.6}(a+2)}:\left(\left(a^{1/2}-b^{1/2}\right)(a-b)^{-2/5}\right)^{-1}
$$

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