
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 two sequences $\{a_n\}$ and $\{b_n\}$ are both arithmetic sequences, and $a_1=25$, $b_1=125$, $a_2+b_2=150$, find the value of the 2006th term of the sequence $\{a_n+b_n\}$.

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