
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
Determine the values of $a$ for which the equation $\log_{10}(a^2 - 20a) = 2$ holds true.
**A)** $20, -5$  
**B)** $10 + 10\sqrt{2}, 10 - 10\sqrt{2}$  
**C)** $30, 10$  
**D)** $15 \pm \sqrt{305}/2$

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