
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
For a positive integer $n$, define $F(n)=\left\{\begin{array}{l}{{n}^{2}(0＜n＜10)}\\{f(n)(n≥10)}\end{array}\right.$ where $f(n)$ represents the sum of the squares of the first and last digits of $n$. For example, $F(6)=6^{2}=36$, $F(123)=f(123)=1^{2}+3^{2}=10$. Define $F_{1}(n)=F(n)$, $F_{k+1}(n)=F(F_{k}(n))$. For example, $F_{1}(123)=F(123)=10$, $F_{2}(123)=F(F_{1}(123))=F(10)=f(10)=1^{2}+0^{2}=1$. Find $F_{15}(4)=\_\_\_\_\_\_$.

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