
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 vectors $\overset{→}{a}=(\cos x,-1+\sin x)$ and $\overset{→}{b}=(2\cos x,\sin x)$,

(1) Express $\overset{→}{a}·\overset{→}{b}$ in terms of $\sin x$.

(2) Find the maximum value of $\overset{→}{a}·\overset{→}{b}$ and the corresponding value of $x$.

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