
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 the function $f(x) = (x+a)\ln x$, and let $g(x) = \frac{x^2}{e^x}$. It is known that the tangent to the curve $y = f(x)$ at the point $(1, f(1))$ is perpendicular to the line $x + 2y - 1 = 0$.
(Ⅰ) Find the value of $a$;
(Ⅱ) Let the function $m(x) = \min\{f(x), g(x)\}$ (where $\min\{p, q\}$ denotes the smaller value between $p$ and $q$). Find the maximum value of the function $m(x)$.

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