
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 $\{a_n\}$ satisfying $a_1=a_2=1$, $a_{n+2}=a_{n}+2(-1)^{n}$, $(n\in\mathbb{N}^*)$.

(Ⅰ) Write down the values of $a_5$ and $a_6$;  
(Ⅱ) Let $b_n=a_{2n}$, find the general formula for $\{b_n\}$;  
(Ⅲ) Denote the sum of the first $n$ terms of the sequence $\{a_n\}$ as $S_n$, find the minimum value of the sum of the first $n$ terms of the sequence $\{S_{2n}-18\}$, denoted as $T_n$.

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