
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 all roots of the equation \( a^{x} + 2x - 4 = 0 \) are \( u_{1}, u_{2}, \cdots, u_{k} \), and all roots of the equation \( \log_{a}(2x) + x - 2 = 0 \) are \( v_{1}, v_{2}, \cdots, v_{l} \), calculate the value of \( \frac{u_{1} + u_{2} + \cdots + u_{k} + v_{1} + v_{2} + \cdots + v_{l}}{k + l} \).

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