
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
Let \( x \) be the number of candies Piglet has, \( y \) the number of candies Winnie the Pooh has, and \( n \) the number of candies Winnie would take from Piglet. The system is:

\[
\begin{cases}
y + n = 4(x - n) \\
x + 90 = 5(y - 90)
\end{cases}
\]

Later, it is transformed into:

\[
\begin{cases}
x = 5y - 540 \\
y + n = 20y - 2160 - 4n
\end{cases}
\]

From which:

\[ 
y = 113 + \frac{5n + 13}{19}
\]

Determine the values of \( y \) (which must be a minimum natural number) and \( n \).

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