
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
A factory's total production value has been increasing for two consecutive years. The growth rate for the first year is $a$, and the growth rate for the second year is $b$. What is the average annual growth rate for the factory's total production value over these two years?

A) $\frac{a+b}{2}$
B) $\sqrt{ab}$
C) $\sqrt{(a+1)(b+1)}-1$
D) $\sqrt{(a+1)(b+1)}+1$

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