
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 $f(x)=\sin (x+ \frac {π}{6})+ \sin (x- \frac {π}{6})+ \cos x+a$. The maximum value of the function is $1$.

1. Find the interval(s) where the function is strictly increasing.
2. In triangle $ABC$, let $A$, $B$, $C$ be the angles opposite to sides $a$, $b$, $c$ respectively. If $f(A)=1$, $C= \frac {π}{4}$, and $c=2$, find the value of $b$.

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