Putty JailShell can't run command 'cake shell_name'

I went to my .bash_profile and I changed the path to:
PATH=/usr/local/public_html/cake/console:$PATH:$HOME/bin
then I connected through SSH with Putty to my remote linux VPS server
with Hostgator and then I can't run cake bake. What is wrong?

I copied all the activity from the console as follows:

projectf@project.fcaceres.net [~]# cd public_html
projectf@project.fcaceres.net [~/public_html]# cd app
projectf@project.fcaceres.net [~/public_html/app]# ../cake/console/
cake

Welcome to CakePHP v1.3.5 Console
---------------------------------------------------------------
Current Paths:
-app: app
-working: /home/projectf/public_html/app
-root: /home/projectf/public_html
-core: /home/projectf/public_html

Changing Paths:
your working path should be the same as your application path
to change your path use the '-app' param.
Example: -app relative/path/to/myapp or -app /absolute/path/to/myapp

Available Shells:
acl [CORE] i18n [CORE]
api [CORE] schema [CORE]
bake [CORE] testsuite [CORE]
console [CORE]

To run a command, type 'cake shell_name [args]'
To get help on a specific command, type 'cake shell_name help'
projectf@project.fcaceres.net [~/public_html/app]# cake bake
-bash: cake: command not found
projectf@project.fcaceres.net [~/public_html/app]# cake acl
-bash: cake: command not found
projectf@project.fcaceres.net [~/public_html/app]# cake i18n
-bash: cake: command not found
projectf@project.fcaceres.net [~/public_html/app]#

I believe I am not the only person having this problem. Please help us
figure this out.
Thank you

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