Scoring song with multiple sections

[Henry Law]

(Lilypond v2.18.2 under Linux.)

I'm scoring a song which has the form A A B C C.  Two verses go to 
section A, then there are words for a bridge, then two more verses to 
the music of section C.  Or to put it graphically

Chords to section A
Notes of section A
 Verse 1 words
 Verse 2 words

Chords to bridge
Notes of bridge
 Words to bridge

Chords to section C
Notes of section C
 Verse 3 words
 Verse 4 words

I can do section A but I'm struggling with how to make the bridge and 
its words appear on the same staff in subsequent bars.  It seems to me 
that all the stuff to "A A" is simultaneous stuff and should appear in 
<< >>, and then the stuff for the bridge is different simultaneous 
stuff, and should have its own << >>, and therefore coded this:

\score {
  <<
    \new ChordNames \chordsVerseOneTwo
    \new Staff { \melodyVerseOneTwo }
    \addlyrics { \verseOne }
    \addlyrics { \verseTwo }
  >>
  <<
    { \bridge }
    \addlyrics { \bridgeWords }
  >>
  \layout { ... etc

But on the second appearance of "<<" Lily barfs with "syntax error, 
unexpected <<".

Of course it's an schoolboy error (that's the kind of mistake I'm making 
right now) but I've reviewed the learning manual, especially "Music 
expressions explained" and also the snippets without finding the answer. 
 Can someone help me please?
--

Henry Law            Manchester, England