
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 a sequence $\{a_{n}\}$ that satisfies ${a}_{n+2}=\left\{\begin{array}{l}{a}_{n}+2, n \text{ is odd}\\ 2{a}_{n}, n \text{ is even}\end{array}\right.$ and $a_{1}=1$, $a_{2}=2$.<br/>$(1)$ Find the general term $a_{n}$;<br/>$(2)$ Find the sum of the first $n$ terms of the sequence $\{a_{n}\}$ denoted as $T_{n}$.

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