
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 two functions defined on set A, $f(x) = x^2 + 1$, $g(x) = 4x + 1$.
(1) If $A = \{x | 0 \leq x \leq 4\}$, $x \in \mathbb{R}$, find the range of the functions $f(x)$ and $g(x)$ respectively;
(2) If for any $z$ in set A, $f(x) = g(x)$, find the set A.

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