
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 an geometric sequence ${a_n}$ with the first term $a_1=1$ and the common ratio $q (q > 0)$, and if $2a_1$, $\frac{1}{2}a_3$, $a_2$ form an arithmetic sequence, then:

(i) Find the value of $q$.
(ii) If another sequence ${b_n}$ satisfies $b_n = a_n + n$, calculate the sum of the first $n$ terms ${T_n}$ of the sequence ${b_n}$.

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