
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
Given a sequence $\{a_{n}\}$ that satisfies ${a}_{n}=\left\{\begin{array}{l}\frac{2}{n(n+2)}\text{(n is a positive odd number)}\\ \ln(\frac{n+2}{n})\text{(n is a positive even number)}\end{array}\right.$, then the sum of the first $10$ terms of the sequence $\{a_{n}\}$ is ______.

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