
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 $5^{2x}+20 = 12 \cdot 5^x$, find the values of $(x^2+x)$.
**A)** $(\log_5 10)^2 + \log_5 10$ only   
**B)** $(\log_5 2)^2 + \log_5 2$ only    
**C)** $(\log_5 10)^2 + \log_5 10$ or $(\log_5 2)^2 + \log_5 2$   
**D)** $1$ only   
**E)** $0$ only

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