
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 $p$ and $q$ such that $\log p + \log q = \log (p + 2q)$.
**A)** $p = \frac{2q}{q+1}$  
**B)** $p = \frac{2q^2}{q+1}$  
**C)** $p = \frac{2q}{q-1}$  
**D)** $p = \frac{q}{2(q-1)}$  
**E)** $p = \frac{q}{q-1}$

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