
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 hyperbola $\frac{x^{2}}{a-3} + \frac{y^{2}}{2-a} = 1$, with foci on the $y$-axis and a focal distance of $4$, determine the value of $a$. The options are:
A) $\frac{3}{2}$
B) $5$
C) $7$
D) $\frac{1}{2}$

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