
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
A stadium's corner stand has a total of $20$ rows of seats. The seats are arranged in such a way that the first row has $2$ seats, and each subsequent row has $1$ more seat than the previous row. Let $a\_n$ denote the number of seats in the $n$th row.

1. Determine the total number of seats in the stand.
2. Let $S_{20}$ be the sum of the first $20$ terms of the sequence ${2^{n}⋅a_{n}}$. Find the value of ${\log _{2}S_{20}-\log _{2}20}$.

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