
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 $f(x)= \frac{1}{4^{x}} + \frac{a}{2^{x}} +1$, where $a$ is a real constant.

(1) If the minimum value of $f(x)$ is $-7$ when $x\in[-1,0]$, find the value of $a$;

(2) If the inequality $|f(x)|\leqslant 3$ always holds when $x\in[0,+\infty)$, find the range of values for $a$.

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