
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
If it is known that $\log_{10}(a) + \log_{10}(2b) \geq 3$, find the least value that can be taken on by $a + b$.
A) $20$
B) $100$
C) $10\sqrt{5}$
D) $20\sqrt{5}$
E) $25$

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