
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 $f(x)=\sin^{2}x-\cos^{2}x+2 \sqrt {3}\sinx\cosx$, where $x\in\mathbb{R}$.
(1) Find the interval(s) where $f(x)$ is strictly increasing.
(2) In triangle $\triangle ABC$, let $a$, $b$, and $c$ denote the lengths of the sides opposite to angles $A$, $B$, and $C$, respectively. If $f(A)=2$, $c=5$, and $\cos B=\frac{1}{7}$, find the length of side $a$.

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