
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 the function $f(x)=ax^{2}+2x+c$ has its lowest point at $(-1,-2)$.  
$(1)$ Find the solution set of the inequality $f(x) > 7$;  
$(2)$ If for any $x∈[2,4]$, the inequality $f(x-t)\leqslant x-2$ always holds, find the range of the real number $t$.

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