
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 the sum of the first $n$ terms of an arithmetic sequence ${a_n}$ is $S_n$, and $a_7=16$, $S_6=33$. The geometric sequence ${b_n}$ satisfies $b_1=\frac{1}{2}$, and the points $(2, b_2)$, $(1, b_3)$ lie on the line $x-8y=0$.
(1) Find the general term formulas for the sequences ${a_n}$ and ${b_n}$;
(2) Given that the sum of the first $n$ terms of the sequence ${a_n + b_n}$ is $T_n$.

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