
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
$a$, $b$, $c$ are different lines, $α$, $β$, $γ$ are different planes. Determine the number of conclusions that hold true among the following:
① If $a$ is parallel to $b$ and $b$ is parallel to $c$, then $a$ is parallel to $c$.
② If $a$ is perpendicular to $b$ and $b$ is perpendicular to $c$, then $a$ is parallel to $c$.
③ If $α$ is perpendicular to $β$ and $β$ is perpendicular to $γ$, then $α$ is parallel to $γ$.
④ If $α$ is perpendicular to $β$ and $α$ intersects $β$ at $a$, and $b$ is perpendicular to $a$, then $b$ is perpendicular to $β$.

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