
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 \in \mathbb{R}\\), the function \\(f(x) = \left| x + \frac{4}{x} - a \right| + a\\) has a maximum value of \\(5\\) on the interval \\([1,4]\\). The range of the real number \\(a\\) is ______________.

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