
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
Suppose there are three lines in space, and there are five assertions:
If $a \perp b$ and $b \perp c$, then $a \perp c$;
If lines $a$ and $b$ are skew lines, and lines $b$ and $c$ are skew lines, then lines $a$ and $c$ are also skew lines;
If line $a$ intersects line $b$, and line $b$ intersects line $c$, then line $a$ intersects line $c$;
If line $a$ is coplanar with line $b$, and line $b$ is coplanar with line $c$, then line $a$ is coplanar with line $c$;
If $a \parallel b$ and $b \parallel c$, then $a \parallel c$;
Determine the number of correct assertions.

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