
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 vector $\overrightarrow{b}$ is in the opposite direction to vector $\overrightarrow{a}=(1,-2)$, and $|\overrightarrow{b}|=3\sqrt{5}$,  
(1) Find the coordinates of vector $\overrightarrow{b}$;  
(2) If $\overrightarrow{c}=(2,3)$, find the value of $(\overrightarrow{c}-\overrightarrow{a})\cdot(\overrightarrow{c}-\overrightarrow{b})$.

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