
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 that the function $f(x)$ is an even function on the real line $\mathbb{R}$. When $x \leq 0$, $f(x) = 4^{-x} - a \cdot 2^{-x}$ ($a>0$).
(Ⅰ) Find the expression for $f(x)$ on the interval $(0, +\infty)$.
(Ⅱ) Find the minimum value of $f(x)$ on the interval $(0, +\infty)$.

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