
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
Given a positive number $a$ and another number $b = a + 1$. Let $A.M.$ be their arithmetic mean and $G.M.$ their positive geometric mean. Then $A.M.$ minus $G.M.$ is always less than:
1) What expression?
A) $\dfrac{1}{a}$
B) $\dfrac{3}{2}$
C) $\dfrac{1}{2}$
D) $\dfrac{1}{4a}$
E) $\dfrac{2}{3}$

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