
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
Let $f(x) = \log_{2}(1 + a \cdot 2^{x} + 4^{x})$, where $a$ is a constant.
(Ⅰ) When $f(2) = f(-1) + 4$, find the value of $a$;
(Ⅱ) When $x \in [1, +\infty)$, the inequality $f(x) \geq x - 1$ always holds. Find the range of values for $a$.

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