
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 $f(x)=\cos \left(2x-\frac{4π}{3}\right)+2\cos^2 x$.

(1) Find the equation of the axis of symmetry for $f(x)$;

(2) In triangle $ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$, respectively. If $f\left(\frac{A}{2}\right)=\frac{1}{2}$ and $b+c=2$, find the minimum possible value of $a$.

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