
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
Let $f(x) = \frac{(4x+a)\ln x}{3x+1}$, and the curve $y = f(x)$ has a tangent line at the point $(1, f(1))$ which is perpendicular to the line $x+y+1=0$.
(Ⅰ) Find the value of $a$;
(Ⅱ) If for any $x \in [1,e]$, $f(x) \leq mx$ always holds, find the range of possible values for $m$.

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