
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 geometric sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, and $2a_n+2a_{n+2}+5S_n=5S_{n+1}$, and $a_1=q > 1$, the sequence $\{b_n\}$ satisfies $\frac {b_n}{a_n}=|\sin \frac {(n+1)\pi}{2}|$. If the sum of the first $m$ terms of the sequence $\{b_n\}$ is $340$, then the value of $m$ is ______.

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