
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
Find the value of
$$
\binom{6}{1} 2^{1}+\binom{6}{2} 2^{2}+\binom{6}{3} 2^{3}+\binom{6}{4} 2^{4}+\binom{6}{5} 2^{5}+\binom{6}{6} 2^{6}.
$$

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