
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 that function $f(x)$ is an odd function defined on $\mathbb{R}$, and $g(x) = f(x + 1) + 5$. If $g'(x)$ is the derivative of $g(x)$ and $\forall x \in \mathbb{R}$, $g'(x) > 2x$, then the solution set for $g(x) < x^2 + 4$ is _____.

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