
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
Solve the equation:

a) $\log _{3}(x-2)+\log _{3} x=\log _{3} 8$;

b) $\lg (x-9)+2 \lg \sqrt{2 x-1}=2$;

c) $\frac{1}{2} \log _{5}(x+5)+\log _{5} \sqrt{x-3}=\frac{1}{2} \log _{5}(2 x+1)$.

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