
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 the function $f(x)=2\cos x(\sin x-\cos x)+1$.
(1) Find the smallest positive period and the interval where the function is strictly increasing.
(2) In $\triangle ABC$, the acute angle $A$ satisfies $f(A)=1$, $b= \sqrt {2}$, $c=3$, find the value of $a$.

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