
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
(1) Find the value of $\lg 4 + \lg 50 - \lg 2$;
(2) If real numbers $a$ and $b$ satisfy $1 + \log_{2}a = 2 + \log_{3}b = \log_{6}(a + b)$, find the value of $\frac{1}{a} + \frac{1}{b}$.

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