
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 $f(x)=1+a\left( \dfrac {1}{2}\right)^{x}+\left( \dfrac {1}{4}\right)^{x}$  
$(1)$ When $a=1$, solve the inequality $f(x) > 7$;  
$(2)$ If for any $x\in[0,+\infty)$, $f(x)\leqslant 3$ always holds, find the range of the real number $a$.

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