
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
Consider the triangular array where each row begins and ends with the row number and interior numbers are obtained by multiplying the two adjacent numbers in the previous row by 0.5 and then adding them. Rows 1 through 5 are constructed and shown.

\[ 
\begin{array}{ccccccccc}
& & & & 1 & & & & \\
& & & 1.5 & & 1.5 & & & \\
& & 2 & & 2.25 & & 2 & & \\
& 2.5 & & 4.25 & & 4.25 & & 2.5 & \\
3 & & 6.75 & & 8.5 & & 6.75 & & 3
\end{array}
\]

Find the sum of the numbers in the 10th row. Your answer should be in simplified form.

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