
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
It is known that the graph of the function $f(x) = a \cdot 2^x + b$ passes through points $A(1, \frac {3}{2})$ and $B(2, \frac {5}{2})$.  
(1) Find the explicit expression for the inverse function $y = f^{-1}(x)$.  
(2) If $F(x) = f^{-1}(2^{x-1}) - \log_{ \frac {1}{2}}f(x)$, find the range of values of $x$ for which $F(x) \leq 0$.

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