
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 an arithmetic sequence $\{a_n\}$ satisfies $a_3=7$ and $a_5+a_7=26$. If $b_n= \frac {1}{a_n\cdot a_{n+1}}$ $(n\in\mathbb{N}^*)$, then the sum of the first $10$ terms of the sequence $\{b_n\}$, denoted as $S_{10}=$ ______.

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