
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 a moving point \\(P(x,y)\\) on the ellipse \\(\dfrac{x^2}{25}+\dfrac{y^2}{16}=1\\), if point \\(A\\) has coordinates \\((3,0)\\), \\(|\overrightarrow{AM}|=1\\), and \\(\overrightarrow{PM}\cdot \overrightarrow{AM}=0\\), then the minimum value of \\(|\overrightarrow{PM}|\\) is \_\_\_\_\_\_\_\_.

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