
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 three numbers $(a-1)$, $(a+1)$, $(a+5)$ form a geometric sequence, and their reciprocals rearranged happen to be the first three terms of an increasing geometric sequence ${a_{n}}$, determine the maximum natural number $n$ such that the inequality $a_{1}+a_{2}+…+a_{n}\leqslant \dfrac {1}{a_{1}}+ \dfrac {1}{a_{2}}+…+ \dfrac {1}{a_{n}}$ holds.

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