
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
If \( f(x) = 5x - 3 \) for \( x \in \{0, 2, 3, 4, 5\} \) and \( g(x) = x^2 - 2x - 3 \) for \( x \in \{-2, -1, 1, 4, 5\} \), then what is the domain of the function \( F(x) = \log f(x) + \frac{1}{\sqrt{g(x}} \)?

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