
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 arithmetic sequence ${a_n}$ satisfies $a_1+a_2=10$, $a_5=a_3+4$.
(1) Find the general term formula for ${a_n}$;
(2) Denote the sum of the first $n$ terms of ${a_n}$ as $S_n$. If $S_{k+1}<2a_k+a_2$, find the value of the positive integer $k$.

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