
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
Given that \( a \neq 1 \), \( b \neq 1 \), \( a > 0 \), and \( b > 0 \), and the relationship \( \log_{a} 2 = \log_{\frac{a}{2}} 4 = \log_{b} 3 \), find the values of \( a \) and \( b \).

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