
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
The sequence $\{a_n\}$ is a geometric progression with $a_n > 0$, $a_1 = \frac{1}{2}$, and the sum of the first $n$ terms is $S_n$. The terms $S_3 + a_3$, $S_5 + a_5$, and $S_4 + a_4$ form an arithmetic sequence.

(I) Find the general term formula for the sequence $\{a_n\}$.
(II) Find the sum of the first $n$ terms $T_n$ of the sequence $\{na_n\}$.

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