
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 {a<sub>n</sub>} is an arithmetic sequence, and log<sub>10</sub>a<sub>1</sub>=0, log<sub>10</sub>a<sub>4</sub>=1.
(1) Find the general term formula for the sequence {a<sub>n</sub>}.
(2) If a<sub>1</sub>, a<sub>k</sub>, a<sub>6</sub> are the first three terms of the geometric sequence {b<sub>n</sub>}, find the value of k and the sum of the first n terms of the sequence {a<sub>n</sub>+b<sub>n</sub>}.

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