
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 function\\(f(x)= \\begin{cases}cx+1,(0 < x < c) \\\\ 2^{ \\frac {x}{c^{2}}}+1,(c\\leqslant x < 1)\\end{cases}\\)，and\\(f(c^{2})= \\dfrac {9}{8}\\)．  
\\((1)\\)Find the value of the real number\\(c\\)；  
\\((2)\\)Solve the inequality\\(f(x) > \\dfrac { \\sqrt {2}}{8}+1\\)．

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