
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
If the solution set of the inequality about \\(x\\), \\(|3x+2|+|3x-1|-t\geqslant 0\\), is \\(\mathbb{R}\\), denote the maximum value of the real number \\(t\\) as \\(a\\).
\\((1)\\) Find \\(a\\);
\\((2)\\) If the positive real numbers \\(m\\), \\(n\\) satisfy \\(4m+5n=a\\), find the minimum value of \\(y= \dfrac {1}{m+2n}+ \dfrac {4}{3m+3n}\\).

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