
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
Simplify the following expression:

$$
\frac{a^{3 / 2}+a^{3 / 4}-\left(\sqrt{a^{3}+2 a^{2}}+\sqrt[4]{a(a+2)^{2}}\right)}{\sqrt{2\left(a+1-\sqrt{a^{2}+2 a}\right)} \cdot\left(a^{2}-a^{5 / 4}+a^{1 / 2}\right)^{-1}}
$$

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