
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
In ancient Egyptian mathematics, there is a unique phenomenon: except for $\frac{2}{3}$, which is represented by a single symbol, other fractions are written as the sum of several unit fractions. For example, $\frac{2}{5}=\frac{1}{3}+\frac{1}{15}$. This can be understood as follows: suppose there are two loaves of bread to be shared equally among $5$ people. Each person would not get enough with $\frac{1}{2}$, and with $\frac{1}{3}$, there would be a remainder of $\frac{1}{3}$. If this $\frac{1}{3}$ is then divided among $5$ people, each person gets $\frac{1}{15}$, so each person gets $\frac{1}{3}+\frac{1}{15}$ in total. The decomposition of fractions in the form of $\frac{2}{n}(n=5,7,9,11,…)$ is as follows: $\frac{2}{5}=\frac{1}{3}+\frac{1}{15}$, $\frac{2}{7}=\frac{1}{4}+\frac{1}{28}$, $\frac{2}{9}=\frac{1}{5}+\frac{1}{45}$, $…$. According to this rule, $(1)\frac{2}{11}=$ \_\_\_\_\_\_, and $(2)\frac{2}{n}=$ \_\_\_\_\_\_ $(n=5,7,9,11,…)$.

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