
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
There are two financial products, "Zhongou Jun Tai" and "Yongying Currency", with annual profits of $S$ and $T$ (in ten thousand yuan), respectively, when investing in these two financial products. Their relationship with the investment amount $x$ (in ten thousand yuan) is described by the empirical equations: $S=\frac{x}{5}$, $T=\frac{2\sqrt{x}}{5}$. If $5$ ten thousand yuan is invested in these two financial products, the maximum annual profit that can be obtained is ______ ten thousand yuan.

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