
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 \\(f(x)=-\dfrac{\sqrt{2}}{2}\sin (2x+\dfrac{\pi }{4})+2\\), find:

\\((1)\\) The equation of the axis of symmetry and the interval of monotonic increase for \\(f(x)\\);

\\((2)\\) If the equation \\(\left| f(x)-m \right|\leqslant 1\\) always holds for \\(x\in \left[0,\dfrac{\pi }{2}\right]\\), find the range of the real number \\(m\\).

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