
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
Point \(P\) is on the right branch of the hyperbola \(\dfrac{x^2}{16} - \dfrac{y^2}{9} = 1\), \(F\) is its right focus, and point \(A(6,0)\). The minimum value of \(|PA|+|PF|\) is (__).

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