
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 functions $f(x)=|x-m|$ and $h(x)=|x-2|+|x+3|$.

$(1)$ If the solution set of the inequality $f(x)\leqslant 3$ is $\{x|-1\leqslant x\leqslant 5\}$, find the value of the real number $m$.

$(2)$ If the equation $x^{2}+6x+h(t)=0$ has solutions, find the range of the real number $t$.

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