
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 the functions \( f(x) = \frac{x^2 + 4x + 3}{x^2 + 7x + 14} \) and \( g(x) = \frac{x^2 - 5x + 10}{x^2 + 5x + 20} \):
1. Find the maximum value of the function \( f(x) \).
2. Find the maximum value of the function \( g(x)^{f(x)} \).

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