
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
For any two non-zero planar vectors $\overrightarrow{m}$, $\overrightarrow{n}$, define an operation "$\ast$" as: $\overrightarrow{m} \ast \overrightarrow{n}= \dfrac{\overrightarrow{m} \cdot \overrightarrow{n}}{\overrightarrow{n} \cdot \overrightarrow{n}}$. If the angle between planar vectors $\overrightarrow{a}$, $\overrightarrow{b}$ is $\theta \in (0, \dfrac{\pi}{4})$, and the values of $\overrightarrow{a} \ast \overrightarrow{b}$ and $\overrightarrow{b} \ast \overrightarrow{a}$ are both elements of the set $\{t|t= \dfrac{k}{2},k\in \mathbb{N}^{*}\}$, then $\overrightarrow{a} \ast \overrightarrow{b} + \overrightarrow{b} \ast \overrightarrow{a}=$ \_\_\_\_\_\_.

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