
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 geometric sequence $\{a_n\}$ is an increasing sequence, and $a_5^2=a_{10}$, $2(a_n+a_{n+2})=5a_{n+1}$, where $n\in\mathbb{N}^*$.  
(Ⅰ) Find $a_n$;  
(Ⅱ) Let $c_n=1-(-1)^na_n$, the solution set of the inequality $c_k \geqslant 2014$ $(1\leqslant k\leqslant 100,k\in\mathbb{N}^*)$ is $M$, find the sum of all $a_k (k\in M)$.

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