
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 the array: \\(( \frac {1}{1}),( \frac {1}{2}, \frac {2}{1}),( \frac {1}{3}, \frac {2}{2}, \frac {3}{1}),( \frac {1}{4}, \frac {2}{3}, \frac {3}{2}, \frac {4}{1}),…,( \frac {1}{n}, \frac {2}{n-1}, \frac {3}{n-2},… \frac {n-1}{2}, \frac {n}{1})\\)
Denote this array as: \\((a_{1})\\), \\((a_{2},a_{3})\\), \\((a_{3},a_{4},a_{5})\\), \\(…\\)
Find the value of \\(a_{2009}=\\) \_\_\_\_\_\_.

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