
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 the function $f(x)$ is defined on $\mathbb{R}$ with a period of $3$, and $f(x)=x^{2}+4$ when $1 \leqslant x \leqslant 3$.

(1) Find the value of $f(5)+f(7)$;

(2) If the equation $f(x)=mx^{2}$ (where $m \in \mathbb{R}$) has real roots in the interval $[4,6]$, find the range of the real number $m$.

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