
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
(1) Given $\log_{18}9=a$, $18^b=5$, express $\log_{36}45$ in terms of $a$ and $b$;  
(2) Given $\overrightarrow{a}=(\sin x, 1)$, $\overrightarrow{b}=(\sin x, \cos x)$, $f(x)= \overrightarrow{a} \cdot \overrightarrow{b}$, find the maximum value of $f(x)$.

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