
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
Let the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ have a point $P(x, y)$ moving along it, and a fixed point $M(a, 0)$ where $0 < a < 3$. If the minimum distance $|PM|$ between $P$ and $M$ is 1, then determine the value of $a$.

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