
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 sequences {a_n} and {b_n} are arithmetic sequences with a common difference of 1, the first terms of the sequences are a_1 and b_1 respectively, a_1 + b_1 = 5, a_1 > b_1, and a_1, b_1 are positive integers. Determine the sum of the first ten terms of the sequence {a_{b_n}}.

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