
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
Given the following three analogical conclusions:
1. If $a, b, c, d \in \mathbb{R}$, and a complex number $a+bi=c+di$, then $a=c$, $b=d$. By analogy, if $a, b, c, d \in \mathbb{Q}$, and $a+b\sqrt{5}=c+d\sqrt{5}$, then $a=c$, $b=d$;
2. Given lines $a, b, c$, if $a \parallel b$ and $b \parallel c$, then $a \parallel c$. By analogy, given vectors $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$, if $\overrightarrow{a} \parallel \overrightarrow{b}$ and $\overrightarrow{b} \parallel \overrightarrow{c}$, then $\overrightarrow{a} \parallel \overrightarrow{c}$;
3. In the same plane, $a, b, c$ are three different lines, if $a \parallel b$ and $b \parallel c$, then $a \parallel c$. By analogy, in space, $\alpha, \beta, \gamma$ are three different planes, if $\alpha \parallel \beta$ and $\beta \parallel \gamma$, then $\alpha \parallel \gamma$.

The number of correct conclusions is ______.

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