
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
The relationship between the temperature of a lizard and the sunlight it receives approximately follows the function: $T(t)=\frac{{120}}{{t+5}}+15$, where $T(t)$ is the temperature of the lizard (unit: $^{\circ}C$), and $t$ is the time after sunset (unit: $\min$). <br/>$(1)$ Find ${T'}(10)$ and explain its practical significance; <br/>$(2)$ At what time $t$ does the instantaneous rate of change of the lizard's body temperature equal $-1^{\circ}C/\min$ (rounded to $0.01$)?

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