
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
Generally, if the graph of a function $f(x)$ is symmetric about the point $(a, b)$, then for any $x$ in the domain, $f(x) + f(2a-x) = 2b$ always holds. Given that the function $f(x) = \frac {4^{x}}{4^{x}+m}$ has a domain of $\mathbb{R}$ and its graph is symmetric about the point $(\frac {1}{2}, \frac {1}{2})$,  
(1) Find the value of the constant $m$;  
(2) Solve the equation in terms of $x$: $\log_{2}[1-f(x)] \cdot \log_{2}[4^{-x}f(x)]=2$.

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