
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 the sequence {a<sub>n</sub>} is an arithmetic sequence with all positive terms, and the sum of its first 9 terms S<sub>9</sub> is $$\frac {9}{2}$$, find the minimum value of $$\frac {1}{a_{2}}$$+ $$\frac {4}{a_{8}}$$.

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