
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 that ${a_n}$ is an arithmetic sequence and ${b_n}$ is a geometric sequence. If $a_1+a_3+a_5+a_7+a_9=50$, $b_4 \cdot b_6 \cdot b_{14} \cdot b_{16}=625$, find the value of $\frac {a_{2}+a_{8}}{b_{10}}$.

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