
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  $a_1,..., a_5 \in R$ ,   $$ \frac{a_1}{k^2 + 1}+ ... +\frac{a_5}{k^2 + 5}=\frac{1}{k^2} $$   for all  $k \in \{2, 3, 4, 5, 6\}$ . Calculate   $$ \frac{a_1}{2}+... +\frac{a_5}{6}. $$  

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