
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 proposition $p: \forall x\in \{x\left|\right.-3 \lt x \lt 1\}$, the inequality $x^{2}+4x+9-m \gt 0$ always holds true; proposition $q: \exists x\in \{x\left|\right.x \gt 0\}$, $x^{2}-2mx+1 \lt 0$ holds true.<br/>$(1)$ If proposition $p$ is a true proposition, find the range of real number $m$;<br/>$(2)$ If exactly one of the propositions $p$ and $q$ is true, find the range of real number $m$.

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