
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 $f(x)= \frac{1}{4^{x}} - \frac{\lambda}{2^{x-1}} + 3$ where $-1\leqslant x\leqslant 2$.
(1) If $\lambda = \frac{3}{2}$, find the range of the function $f(x)$.
(2) If the minimum value of the function $f(x)$ is 1, find the value of the real number $\lambda$.

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