
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 the identity: \\(\sqrt{1+2 \sqrt{1+3 \sqrt{1+4 \sqrt{1+5 \sqrt{1+\cdots}}}}}=3 .\\) Find the value of \\(\sqrt{1+3 \sqrt{1+4 \sqrt{1+5 \sqrt{1+6 \sqrt{1+\cdots}}}}} =\\)\_\_\_\_ and make a conjecture about the value of \\(\sqrt{1+n \sqrt{1+(n+1) \sqrt{1+(n+2) \sqrt{1+(n+3) \sqrt{1+\cdots}}}}} =\\)\_\_\_\_\_\_\_\\(.(n∈N\*)\\)

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