
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 the arithmetic sequence $\{a_n\}$, it is given that $a_9= \frac {1}{2}a_{12}+6$ and $a_2=4$. Let the sum of the first n terms of the sequence $\{a_n\}$ be $S_n$. Calculate the sum of the first $10$ terms of the sequence $\left\{ \frac {1}{S_n} \right\}$.

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