
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 $g(x)=\sqrt{x}+1$ and $h(x)=\frac{1}{x+3}$, where $x \in (-3, a]$, and $a$ is a positive constant. Let $f(x)=g(x)\cdot h(x)$.

(1) Find the expression for $f(x)$ and its domain.
(2) When $a=\frac{1}{4}$, find the range of $f(x)$.

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