
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 function $f(x) = \log_{4}(2x + 3 - x^2)$.  
(1) Find the domain and intervals of monotonicity for $f(x)$.  
(2) Find the maximum value of $f(x)$, and the value of $x$ at which the maximum occurs.  
(3) Let $g(x) = \log_{4}[(a + 2)x + 4]$, if the inequality $f(x) \leq g(x)$ holds for all $x \in (0, 3)$, find the range of the real number $a$.

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