
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 a function $f(x)$ that satisfies $f(x+1)=x^2 - \frac{1}{3}f(3)$,
(1) Find the explicit expression for $f(x)$;
(2) When $x \in \left(-2, -\frac{1}{2}\right)$, the inequality $f(a)+4a < (a+2)f(x^2)$ is always true, determine the range for the value of $a$.

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