
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 functions $f(x) = |2x - 3| + 3$ and $g(x) = 2x + \frac{a}{x}, a > 0$.

1. Solve the inequality $f(x) \leq 3x$.
2. Let $M = {y \mid y = f(x)}$ and $N = {y \mid y = g(x)}$. If $M \subseteq N$, find the range of values for $a$.

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