
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
In the sequences $\{a_n\}$ and $\{b_n\}$, $a_1=1$, $a_{n+1}=a_n+2$, $b_1=3$, $b_2=7$, and the geometric sequence $\{c_n\}$ satisfies $c_n=b_n-a_n$.  
(I) Find the general formulas for the sequences $\{a_n\}$ and $\{c_n\}$.  
(II) If $b_6=a_m$, find the value of $m$.

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