
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 that $F$ is the left focus of the ellipse $E: \frac{{x}^{2}}{16} + \frac{{y}^{2}}{7} = 1$, point $P$ is a point on $E$, and point $M$ is a point on the circle $C: \left(x-1\right)^{2} + \left(y-1\right)^{2} = 1$, then the minimum value of $|PF| + |PM|$ is ______.

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