
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 positive real numbers $m$ and $n$ satisfying $m+n=1$, making $\dfrac{1}{m}+ \dfrac{16}{n}$ reach its minimum value, and the curve $y=x^{a}$ passing through the point $P\left( \dfrac{m}{5}, \dfrac{n}{4}\right)$, determine the value of $a$.

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