
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 geometric sequence \\(\{a_n\}(n\in\mathbb{N}^*)\\) where each term is positive, and it satisfies \\(a_7=a_6+2a_5\\). If there exist two terms \\(a_m\\) and \\(a_n\\) such that \\(\sqrt{a_ma_n}=4a_1\\), then the minimum value of \\(\dfrac{1}{m}+\dfrac{4}{n}\\) is \_\_\_\_\_\_.

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