
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 $\[t\]$ represents the greatest integer not exceeding $t$, for example, $\[12.5\]=12$, $\[-3.5\]=-4$, for any real number $x$, let $f\_{1}(x)=\[4x\]$, $g(x)=4x-\[4x\]$, and further let $f\_{2}(x)=f\_{1}\[g(x)\]$.
(1) If $x= \frac {7}{16}$, find $f\_{1}(x)$ and $f\_{2}(x)$;
(2) If $f\_{1}(x)=1$, $f\_{2}(x)=3$ are simultaneously satisfied, find the range of $x$.

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