
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
Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system $xOy$, the equation of circle $C$ is $(x+6)^{2}+y^{2}=25$.

(Ⅰ) Establish a polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, and find the polar equation of $C$;

(Ⅱ) The parametric equation of line $l$ is $\begin{cases} x=t\cos \alpha \\ y=t\sin \alpha \end{cases}$ (where $t$ is the parameter), line $l$ intersects $C$ at points $A$ and $B$, $|AB|=\sqrt{10}$, find the slope of $l$.

Elective 4-5: Inequality Elective

Given the inequality $2|x-3|+|x-4| < 2a$

(Ⅰ) If $a=1$, find the solution set of the inequality;

(Ⅱ) If it is known that the solution set of the inequality is not empty, find the range of values for $a$.

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