
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
For a sequence $\{a_n\}$ where each term is not $0$, it satisfies $\frac {a_{n+1}(a_{n}+a_{n+2})}{2}=a_{n+2}a_{n}$, and $a_{2}=2a_{6}= \frac {1}{5}$. Find the sum of the first $10$ terms of the sequence $\left\{ \frac {1}{a_{n}}\right\}$.

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