
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
Assume \( y_1, y_2, \ldots, y_5 \) are real numbers such that
\[
y_1 + 3y_2 + 6y_3 + 10y_4 + 15y_5 = 3, \\
3y_1 + 6y_2 + 10y_3 + 15y_4 + 21y_5 = 20, \\
6y_1 + 10y_2 + 15y_3 + 21y_4 + 28y_5 = 86, \\
10y_1 + 15y_2 + 21y_3 + 28y_4 + 36y_5 = 225.
\]
Find the value of \( 15y_1 + 21y_2 + 28y_3 + 36y_4 + 45y_5 \).

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