
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
In the "Guess the Number" game, the host picks a target number between \\(1\\) and \\(127\\), keeps it in mind, and asks Xiao Guang to guess it. If Xiao Guang doesn't guess correctly, the host will tell him whether his guess is higher or lower than the target number, and let him guess again until he guesses the target number correctly. Xiao Guang decides to always choose the middle number of the current range to guess the target number, as this method can narrow down the range most effectively.

\\((1)\\) If the host's target number is \\(48\\), how many guesses does Xiao Guang need to correctly guess the target number?

\\((2)\\) If the host randomly picks a target number between \\(1\\) and \\(127\\) with equal probability, on average, how many guesses does Xiao Guang need to correctly guess the target number?

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