
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
Observe the following equations:
$$
\frac {3}{1 \times 2} \times \frac {1}{2}=1- \frac {1}{2^{2}},
$$
$$
\frac {3}{1 \times 2} \times \frac {1}{2}+ \frac {4}{2 \times 3} \times \frac {1}{2^{2}}=1- \frac {1}{3 \times 2^{2}},
$$
$$
\frac {3}{1 \times 2} \times \frac {1}{2}+ \frac {4}{2 \times 3} \times \frac {1}{2^{2}}+ \frac {5}{3 \times 4} \times \frac {1}{2^{3}}=1- \frac {1}{4 \times 2^{3}},
$$
$$
...
$$
From the above equations, find the value of:
$$
\frac {3}{1 \times 2} \times \frac {1}{2}+ \frac {4}{2 \times 3} \times \frac {1}{2^{2}}+...+ \frac {7}{5 \times 6} \times \frac {1}{2^{5}}=
$$
_______ .

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