
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
In the rectangular coordinate system $(xOy)$, the slope of line $l$ is $1$, and its intercept on the $y$-axis is $a-\frac{3}{4}$. The standard equation of circle $C$ is ${(x-3)}^{2}+{(y-3)}^{2}=4$. Establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis.

(I) Find the polar equations of line $l$ and circle $C$;

(II) If the ray $\theta=\frac{\pi}{3}(\rho > 0)$ intersects line $l$ at point $M$ and circle $C$ at points $A$ and $B$, and point $M$ is exactly the midpoint of segment $AB$, find the value of $a$.

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